Use Special Rule 5 Bogging Down of Hit the Dirt for both Infantry and Vehicles crossing significant rivers (as opposed to Streams). Stands will bog down when attempted to cross a river on 4-, unbogging on 5+. Infantry never become permanently mired, but vehicles do so on a 1.
An alternative suggested by Tim Marshal
Excerpt from Tim Marshall on the Crossfire discussion forum. Apply to real rivers as opposed to streams.
As a point of interest, what we do for crossing rivers is have the enemy roll for “getting stuck” or foundering… It usually works like this:
A river crossing area is said to invoke “reactive fire” from the enemy. 1 to 4 dice might be used, depending on the depth, current, etc, and whether a vehicle is crossing versus infantry – for example, in our “standard” crossing, it’s 2 dice versus dismounted infantry and small vehicle, 3 versus heavier vehicles (reflecting on how easily a vehicle can be stuck).
The results of “hits” vary according to scenario and how rough the river really is:
Two hits/Suppression means the crossing squad/vehicle is foundered/stuck. Depending on how much of an obstacle we want the river to be, the result is one of two things:
1) the squad/vehicle cannot move the rest of this initiative. When this option is used, single hits/pins are ignored and the phasing player does not lose initiative;
2) the squad/vehicle must rally to be able to proceed. In this case, we let pins stop the crossers, while suppression will pass initiative to the other side.